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%I #12 Jan 12 2019 04:15:00
%S 1,3,21,271,5065,122811,3651997,128566663,5227782161,241072839667,
%T 12430169195941,708612945554559,44253858433505497,3004570398043291819,
%U 220341964157226260525,17357760973540312138231,1461813975265547356467745,131061164660246579394042339
%N a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 2^k * k^k.
%H Seiichi Manyama, <a href="/A277454/b277454.txt">Table of n, a(n) for n = 0..351</a>
%F E.g.f.: exp(x)/(1+LambertW(-2*x)).
%F a(n) ~ exp(exp(-1)/2) * 2^n * n^n.
%t Table[1+Sum[Binomial[n, k]*2^k*k^k, {k, 1, n}], {n, 0, 20}]
%t CoefficientList[Series[E^x/(1+LambertW[-2*x]), {x, 0, 20}], x] * Range[0, 20]!
%o (PARI) {a(n) = sum(k=0, n, binomial(n, k)*(2*k)^k)} \\ _Seiichi Manyama_, Jan 12 2019
%Y Cf. A086331, A277456.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Oct 16 2016
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